# Dimensional analysis of two-dimensional turbulence

## TL;DR

This paper uses dimensional analysis to explore the scaling laws, energy spectra, and cascade behaviors in two-dimensional turbulence, including energy condensates and inverse cascades, in both forced and decaying scenarios.

## Contribution

It provides a comprehensive dimensional analysis of 2D turbulence, highlighting the properties of energy spectra, condensates, and inverse cascades in various conditions.

## Key findings

- Characterization of energy spectra at different scales
- Analysis of energy condensate formation in finite systems
- Insights into inverse cascade phenomena in decaying turbulence

## Abstract

We study the scaling properties of two-dimensional turbulence using dimensional analysis. In particular, we consider the energy spectrum both at large and small scales and in the "inertial ranges" for the cases of freely decaying and forced turbulence. We also investigate the properties of an "energy condensate" at large scales in spatially finite systems. Finally, an analysis of a possible inverse cascade in freely decaying turbulence is presented.